3/2+13/6+37/12+81/20+151/30+253/42+393/56+577/72+730/81+1101/110怎么简便运算

问题描述:

3/2+13/6+37/12+81/20+151/30+253/42+393/56+577/72+730/81+1101/110怎么简便运算

3/2+13/6+37/12+81/20+151/30+253/42+393/56+577/72+730/81+1101/110
=1+1/2+2+1/6+3+1/12+4+1/20+5+1/30+6+1/42+7+1/56+8+1/72+9+1/81+10+1/110
=(1+2+3+4+5+6+7+8+9+10)+(1/2+1/6+...+1/110)
=55+(1/1×2+1/2×3+1/3×4+1/4×5+1/5×6+1/6×7+1/7×8+1/8×9+1/9×10+1/10×11)
=55+(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11)
=55+1-1/11=55+10/11=615/11.